If it fits the style of the rest of the video, I'll use a subtle film burn as a last resort after I've tried other transitions/clip arrangements, but nothing is working quite right and I want to move on. Typically, I'll combine them with some other distortion effect(s) to make it look a little more original. In the past, I've also used them to hide certain areas of the video or segments of the clip that don't look right (after trying to change other things first). The key is to be subtle though -- don't make them obnoxiously long and opaque/bright. By the time a viewer's brain would notice the effect and think "oh, that's a film burn," it really should be long gone, at least in my opinion. I think they can be used tastefully, but a lot of people are not big fans of the burn.
I think it'd be pretty sweet if I dated a 16 year old. -bock